The religious leaders come from across the spectrum, but hail overwhelmingly from Judaism's Conservative and Reform streams as well as other progressive Jewish movements, a spokesperson said.
"We encourage the members of the Senate and the House of Representatives to endorse this agreement," the 340 rabbis wrote in a letter to Congress distributed by Ameinu, a progressive charitable Jewish organization.
"We are deeply concerned with the impression that the leadership of the American Jewish community is united in opposition to the agreement," the rabbis added.
The agreement, finalized last month after more than a year of intense negotiations, would roll back Iran's nuclear program in exchange for an easing of crippling economic sanctions.
Also Read
Israeli Prime Minister Benjamin Netanyahu is strongly opposed to the deal. He argues it will fail to block Iran's path to nuclear weapons that could be used to target the Jewish state.
Two weeks ago Netanyahu personally called on US Jewish groups to thwart the White House-backed deal. He made his appeal on a webcast hosted by Jewish American groups, which said it reached some 10,000 people.
Progressive group J Street supports it.
The American Jewish Committee, a leading Jewish advocacy organization, has come out opposed, as has the influential American Israel Public Affairs Committee, which is reportedly spending more than USD 20 million in efforts to rally opposition to the deal.
Among the rabbis who signed the congressional letter, 49 are from New York, the state represented by senior Senate Democrat Chuck Schumer, who earlier this month announced he will oppose the accord when it comes up in Congress in September.
On Tuesday another influential Democrat, Senator Robert Menendez, gives a speech on the Iran nuclear accord and will announce whether he will vote for or against it.